In the MCU, the way that time travel works is different than, say, Back to the Future. All time travel stories kind of make up their own rules.

When the Avengers time traveled, they basically just jumped into a different universe, at the time and place where they wanted to be. So they go from Universe A to Universe B, and then when they want to go home, they can bounce back to Universe A So nothing they did in that different universe would directly affect their current universe. If they went to some random person's house (John Smith) in Universe B and killed him, for example, that wouldn't affect Universe A John Smith at all.

So no matter how much trouble they got into in their mission, nothing they could do in any of those parallel worlds would affect Universe A. Except, as it turns out, that they managed to let the bad guys from another world come into Universe A, and that caused some issues.